Question

HELP The minute hand of a clock is 5 inches long. to the the nearest tenth of an inch, how far does the tip of the minute hand travel as the tie progress from 12:00 to 12:35?

Round answer to nearest whole number.
It travels ____ inches

Answer 1

18.326 inches

Explanation:

The question is basically asking us to find the arc length that the tip of the minute hand travels. The formula for an arc length is S=θr. So we need th find the angle that the minute hand passes through. We know that there is 360 degrees in a cicle and there is 12 stops around a clock, so divide 360 by 12 to find the degrees the minute hand travels every 5 minutes. We ge that every 5 minutes the hand travels 30 degrees, and 35 minutes is 7*5 so we multiple 30*7 to find the angular displacement, and we get 210 degrees. This equation uses radians though so we have to convert, which can be done doing
`(210)/(1) *(\pi )/(180)`, and we ge that θ is
`(7\pi )/(6)` so (
`(7\pi )/(6)`)(5)= 18.326 inches